To determine Check the pipe condition whether water is leak out or air enter the pipe when the following case Velocity of water at 5 m/s Velocity of water at 0.5 m/s Explanation Write the expression for the friction factor using the energy balance equation. p 1 γ + V 1 2 2 g + z 1 = p 2 γ + V 2 2 2 g + z 2 + h L (I) Here, the pressure at point 1 is p 1 , the velocity at point 1 is V 1 , the elevation at point 1 is z 1 , the pressure at point 2 is p 2 , the velocity at point 2 is V 2 , the elevation at point 2 is z 2 and the head loss is h L . Write the expression for the major head loss. h L = f l v 2 2 g D (II) Consider the steady state system so the velocity remains constant throughout the pipe. V 1 = V 2 = V (III) Since the water flows to atmosphere at outlet of the pipe so the pressure at the outlet is zero. p 2 = 0 Consider the outlet point as datum so the initial datum height is zero and the inlet datum height is equal to the length of the pipe. z 1 = l = 4 m . z 1 = 0 Substitute 0 for p 2 and z 1 , substitute l for z 1 and Substitute equation (II) and (III) iin equation p 1 γ + V 2 2 g + l = ( 0 ) + V 2 2 g + 0 + f l v 2 2 g D p 1 ρ g = f l v 2 2 g D − l p 1 = f l v 2 2 D ( ρ ) − ρ g l (IV) Write the equation for Reynolds number. Re = V D ν (V) Here, the Reynolds number is Re , the velocity of the fluid is V and the kinematic viscosity of fluid is ν . Conclusion: Refer table B.1, “Physical properties of water” at a temperature of 20 ° C , ν = 1.004 × 10 − 6 m 2 /s For the case (1), When velocity is 5 m/s, Substitute 5 m/s for V , 10 mm for D , and 1.004 × 10 − 6 m 2 /s for ν in equation (VII). Re = ( 5 m/s ) ( 10 mm ) 1.004 × 10 − 6 m 2 /s Re = ( 5 m/s ) ( 10 mm × 1 m 1000 mm ) 1.004 × 10 − 6 m 2 /s = 4..46 × 10 4 > 4000 Thus, the flow in the pipe is turbulent flow. Refer the table 8.1, “Equivalent Roughness for New Pipes”, for the galvanized iron pipe. ε = 0.15 mm Calculate the relative roughness for the given pipe. ε D = 0.15 mm 10 mm = 0.015 Refer figure 8.20 “Friction factor as a function of Reynolds number and relative roughness for round pipes—the Moody chart” Friction factor for 4..46 × 10 4 and 0.015, f = 0.045 Substitute 0.045 for f , 4 m for l , 5 m/s for v , 10 mm for D , 999 kg/m 3 for ρ , 9

Munson, Young and Okiishi's Fundamentals of Fluid Mechanics, Binder Ready Version

8th Edition

ISBN: 9781119080701

Author: Philip M. Gerhart, Andrew L. Gerhart, John I. Hochstein

Publisher: WILEY

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Chapter 8.4, Problem 36P

To determine

Check the pipe condition whether water is leak out or air enter the pipe when the following case

Velocity of water at 5 m/s

Velocity of water at 0.5 m/s

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Chapter 8.4, Problem 35P

Chapter 8.4, Problem 37P

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Munson, Young and Okiishi's Fundamentals of Fluid Mechanics, Binder Ready Version

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